Millimeter-wave synthetic aperture imaging radiometer (SAIR) is a powerful sensor for near-field high-resolution observations. However, the large receiver number and system complexity affect the application of SAIR. To overcome this shortage (receiver number), an accurate imaging algorithm based on compressed sensing (CS) theory is proposed in this paper. For reconstructing the brightness temperature images accurately from the sparse SAIR with fewer receivers, the proposed CS-based imaging algorithm is used to accomplish the sparse reconstruction with fewer visibility samples. The reconstruction is performed by minimizing the l₁ norm of the transformed image. Compared to the FFT-based methods based on Fourier transform, the required receiver number can be further reduced by this method. The simulation results demonstrate that the proposed CS-based method has higher reconstruction accuracy for the sparse SAIR.